The varying compliance (VC) vibration directly reflects the oscillation intensity of a rolling bearing, and it can be fully revealed in the VC resonance. Moreover, we define the bearing vibration intensity as the bearing vibration information in this paper. Besides the rolling element number of the bearing, the rotor eccentricity is also an inevitable influencing factor for the VC vibration. This paper focuses on the VC resonance characteristics in a ball bearing rotor system. An analytical model is established, and the vibration responses of the system are calculated in a large speed range with the consideration of different ball numbers and different rotor eccentricities. The theoretical results show that the VC vibration is clearer in low-speed range where the VC resonance exist, while it is suppressed in high-speed range. In general, the intensity of the VC resonance decreases with the increase of ball numbers and is not sensible to the rotor eccentricities in low-speed range. Finally, a ball bearing rotor experiment system is setup, the VC resonance is clearly detected, and the high-quality bearing vibration information is obtained. The experimental results qualitatively agree with the theoretical results.
Issue Section:
Applications
Keywords:
Bearings
References
1.
Sunnersjö
, C. S.
, 1978
, “Varying Compliance Vibrations of Rolling Bearings
,” J. Sound Vib.
, 58
(3
), pp. 363
–373
.2.
Fukata
, S.
, Gad
, E. H.
, Kondou
, T.
, Ayabe
, T.
, and Tamura
, H.
, 1984
, “On the Radial Vibration of Ball Bearings: Computer Simulation
,” Trans. Jpn. Soc. Mech. Eng. C
, 50
(457
), pp. 1703
–1708
.3.
Mevel
, B.
, and Guyader
, J. L.
, 1993
, “Routes to Chaos in Ball Bearings
,” J. Sound Vib.
, 162
(3
), pp. 471
–487
.4.
Mevel
, B.
, and Guyader
, J. L.
, 2008
, “Experiments on Routes to Chaos in Ball Bearings
,” J. Sound Vib.
, 318
(3
), pp. 549
–564
.5.
Tiwari
, M.
, Gupta
, K.
, and Prakash
, O.
, 2000
, “Effect of Radial Internal Clearance of a Ball Bearing on the Dynamics of a Balanced Horizontal Rotor
,” J. Sound Vib.
, 238
(5
), pp. 723
–756
.6.
Tiwari
, M.
, Gupta
, K.
, and Prakash
, O.
, 2000
, “Dynamic Response of an Unbalanced Rotor Supported on Ball Bearings
,” J. Sound Vib.
, 238
(5
), pp. 757
–779
.7.
Tiwari
, M.
, Gupta
, K.
, and Prakash
, O.
, 2002
, “Experimental Study of a Rotor Supported by Deep Groove Ball Bearing
,” Int. J. Rotating Mach.
, 8
(4
), pp. 243
–258
.8.
Bai
, C.-Q.
, Xu
, Q.-Y.
, and Zhang
, X.-L.
, 2006
, “Nonlinear Stability of Balanced Rotor Due to Effect of Ball Bearing Internal Clearance
,” Appl. Math. Mech.
, 27
(2
), pp. 175
–186
.9.
Ghafari
, S. H.
, Abdel-Rahman
, E. M.
, Golnaraghi
, F.
, and Ismail
, F.
, 2010
, “Vibrations of Balanced Fault-Free Ball Bearings
,” J. Sound Vib.
, 329
(9
), pp. 1332
–1347
.10.
Zhang
, Z.
, Chen
, Y.
, and Li
, Z.
, 2015
, “Influencing Factors of the Dynamic Hysteresis in Varying Compliance Vibrations of a Ball Bearing
,” Sci. China Technol. Sci.
, 58
(5
), pp. 775
–782
.11.
Zhang
, Z.
, Chen
, Y.
, and Cao
, Q.
, 2015
, “Bifurcations and Hysteresis of Varying Compliance Vibrations in the Primary Parametric Resonance for a Ball Bearing
,” J. Sound Vib.
, 350
, pp. 171
–184
.12.
Jin
, Y.
, Yang
, R.
, Hou
, L.
, Chen
, Y.
, and Zhang
, Z.
, 2017
, “Experiments and Numerical Results for Varying Compliance Vibrations in a Rigid-Rotor Ball Bearing System
,” ASME J. Tribol.
, 139
(4
), p. 041103
.13.
Villa
, C.
, Sinou
, J. J.
, and Thouverez
, F.
, 2008
, “Stability and Vibration Analysis of a Complex Flexible Rotor Bearing System
,” Commun. Nonlinear Sci. Numer. Simul.
, 13
(4
), pp. 804
–821
.14.
Gupta
, T.
, Gupta
, K.
, and Sehgal
, D.
, 2011
, “Instability and Chaos of a Flexible Rotor Ball Bearing System: An Investigation on the Influence of Rotating Imbalance and Bearing Clearance
,” ASME J. Eng. Gas Turbines Power
, 133
(8
), p. 82501
.15.
Hou
, L.
, Chen
, Y.
, Cao
, Q.
, and Zhang
, Z.
, 2015
, “Turning Maneuver Caused Response in an Aircraft Rotor-Ball Bearing System
,” Nonlinear Dyn.
, 79
(1
), pp. 229
–240
.16.
Hou
, L.
, Chen
, Y.
, Cao
, Q.
, and Lu
, Z.
, 2016
, “Nonlinear Vibration Analysis of a Cracked Rotor-Ball Bearing System During Flight Maneuvers
,” Mech. Mach. Theory
, 105
, pp. 515
–528
.17.
Hou
, L.
, Chen
, Y.
, Fu
, Y.
, Chen
, H.
, Lu
, Z.
, and Liu
, Z.
, 2017
, “Application of the HB-AFT Method to the Primary Resonance Analysis of a Dual-Rotor System
,” Nonlinear Dyn.
, 88
(4
), pp. 2531
–2551
.18.
Akturk
, N.
, Uneeb
, M.
, and Gohar
, R.
, 1997
, “The Effects of Number of Balls and Preload on Vibrations Associated With Ball Bearings
,” ASME J. Tribol.
, 119
(4
), pp. 747
–753
.19.
Aktürk
, N.
, 1998
, “The Effect of Ball Size Variation on Vibrations Associated With Ball-Bearings
,” Proc. Inst. Mech. Eng. Part J
, 212
(2
), pp. 101
–110
.20.
Akturk
, N.
, 1999
, “The Effect of Waviness on Vibrations Associated With Ball Bearings
,” ASME J. Tribol.
, 121
(4
), pp. 667
–677
.21.
Akturk
, N.
, 2003
, “Some Characteristic Parameters Affecting the Natural Frequency of a Rotating Shaft Supported by Defect-Free Ball Bearings
,” Proc. Inst. Mech. Eng. Part K
, 217
(2
), pp. 145
–151
.22.
Jones
, A. B.
, 1960
, “A General Theory for Elastically Constrained Ball and Radial Roller Bearings Under Arbitrary Load and Speed Conditions
,” J. Basic Eng.
, 82
(2
), p. 309
.23.
Harris
, T. A.
, and Kotzalas
, M. N.
, 2006
, Essential Concepts of Bearing Technology
, CRC Press
, Boca Raton, FL.24.
Walters
, C. T.
, 1971
, “The Dynamics of Ball Bearings
,” ASME J. Tribol.
, 93
(1
), pp. 1
–10
.25.
Gupta
, P. K.
, 1979
, “Dynamics of Rolling-Element Bearings—Part I: Cylindrical Roller Bearing Analysis
,” ASME J. Lubr. Technol.
, 101
(3
), pp. 293
–302
.26.
Gupta
, P. K.
, 1979
, “Dynamics of Rolling-Element Bearings—Part III: Ball Bearing Analysis
,” ASME J. Lubr. Technol.
, 101
(3
), pp. 312
–318
.27.
Gupta
, P. K.
, 1984
, Advanced Dynamics of Rolling Elements
, Springer-Verlag
, Berlin.28.
Liew
, A.
, Feng
, N.
, and Hahn
, E. J.
, 2002
, “Transient Rotordynamic Modeling of Rolling Element Bearing Systems
,” ASME J. Eng. Gas Turbines Power
, 124
(4
), p. 984
.29.
De mul
, J. M.
, Vree
, J. M.
, and Maas
, D. A.
, 1989
, “Equilibrium and Associated Load Distribution in Ball and Roller-Bearings Loaded in 5-Degrees of Freedom While Neglecting Friction—Part I: General Theory and Application to Ball Bearings
,” ASME J. Tribol.
, 111
(1
), pp. 142
–148
.30.
De Mul
, J. M.
, Vree
, J. M.
, and Maas
, D. A.
, 1989
, “Equilibrium and Associated Load Distribution in Ball and Roller-Bearings Loaded in 5-Degrees of Freedom While Neglecting Friction—Part 2: Application to Roller-Bearings and Experimental-Verification
,” ASME J. Tribol.
, 111
(1
), pp. 149
–155
.31.
Jang
, G. H.
, and Jeong
, S. W.
, 2002
, “Nonlinear Excitation Model of Ball Bearing Waviness in a Rigid Rotor Supported by Two or More Ball Bearings Considering Five Degrees of Freedom
,” ASME J. Tribol.
, 124
(1
), pp. 82
–90
.32.
Jang
, G.
, and Jeong
, S. W.
, 2004
, “Vibration Analysis of a Rotating System Due to the Effect of Ball Bearing Waviness
,” J. Sound Vib.
, 269
(3–5
), pp. 709
–726
.33.
Jang
, G. H.
, and Jeong
, S. W.
, 2003
, “Stability Analysis of a Rotating System Due to the Effect of Ball Bearing Waviness
,” ASME J. Tribol.
, 125
(1
), pp. 91
–101
.34.
Changqing
, B.
, and Qingyu
, X.
, 2006
, “Dynamic Model of Ball Bearings With Internal Clearance and Waviness
,” J. Sound Vib.
, 294
(1–2
), pp. 23
–48
.35.
Zhang
, X.
, Han
, Q.
, Peng
, Z.
, and Chu
, F.
, 2013
, “Stability Analysis of a Rotor-Bearing System With Time-Varying Bearing Stiffness Due to Finite Number of Balls and Unbalanced Force
,” J. Sound Vib.
, 332
(25
), pp. 6768
–6784
.36.
Zhang
, X.
, Han
, Q.
, Peng
, Z.
, and Chu
, F.
, 2016
, “A Comprehensive Dynamic Model to Investigate the Stability Problems of the Rotor-Bearing System Due to Multiple Excitations
,” Mech. Syst. Signal Process.
, 70–71
, pp. 1171
–1192
.37.
Wang
, L.
, Cui
, L.
, Zheng
, D.
, and Gu
, L.
, 2008
, “Nonlinear Dynamics Behaviors of a Rotor Roller Bearing System With Radial Clearances and Waviness Considered
,” Chin. J. Aeronaut.
, 21
(1
), pp. 86
–96
.38.
Babu
, C. K.
, Tandon
, N.
, Pandey
, R. K.
, Xiao
, H.
, Brennan
, M. J. M. J.
, Shao
, Y.
, and Brennan
, M. J. M. J.
, 2012
, “Vibration Modeling of a Rigid Rotor Supported on the Lubricated Angular Contact Ball Bearings Considering Six Degrees of Freedom and Waviness on Balls and Races
,” ASME J. Vib. Acoust.
, 134
(1
), p. 011006
.39.
Babu
, C. K.
, Tandon
, N.
, and Pandey
, R. K.
, 2014
, “Nonlinear Vibration Analysis of an Elastic Rotor Supported on Angular Contact Ball Bearings Considering Six Degrees of Freedom and Waviness on Balls and Races
,” ASME J. Vib. Acoust.
, 136
(4
), p. 044503
.40.
Harsha
, S. P.
, Sandeep
, K.
, and Prakash
, R.
, 2003
, “Effects of Preload and Number of Balls on Nonlinear Dynamic Behavior of Ball Bearing System
,” Int. J. Nonlinear Sci. Numer. Simul.
, 4
(3
), pp. 265
–278
.41.
Harsha
, S. P.
, Sandeep
, K.
, and Prakash
, R.
, 2004
, “Non-Linear Dynamic Behaviors of Rolling Element Bearings Due to Surface Waviness
,” J. Sound Vib.
, 272
(3–5
), pp. 557
–580
.42.
Harsha
, S. P.
, and Kankar
, P. K.
, 2004
, “Stability Analysis of a Rotor Bearing System Due to Surface Waviness and Number of Balls
,” Int. J. Mech. Sci.
, 46
(7
), pp. 1057
–1081
.43.
Harsha
, S. P.
, 2006
, “Nonlinear Dynamic Analysis of a High-Speed Rotor Supported by Rolling Element Bearings
,” J. Sound Vib.
, 290
(1–2
), pp. 65
–100
.44.
Sopanen
, J.
, and Mikkola
, A.
, 2003
, “Dynamic Model of a Deep Groove Ball Bearing Including Localized and Distributed Defects—Part 1: Theory
,” Proc. Inst. Mech. Eng. Part K
, 217
(3
), pp. 201
–211
.45.
Sawalhi
, N.
, and Randall
, R. B.
, 2008
, “Simulating Gear and Bearing Interactions in the Presence of Faults—Part I: The Combined Gear Bearing Dynamic Model and the Simulation of Localised Bearing Faults
,” Mech. Syst. Signal Process.
, 22
(8
), pp. 1924
–1951
.46.
Sawalhi
, N.
, and Randall
, R. B.
, 2008
, “Simulating Gear and Bearing Interactions in the Presence of Faults—Part II: Simulation of the Vibrations Produced by Extended Bearing Faults
,” Mech. Syst. Signal Process.
, 22
(8
), pp. 1952
–1966
.47.
Sassi
, S.
, Badri
, B.
, and Thomas
, M.
, 2007
, “A Numerical Model to Predict Damaged Bearing Vibrations
,” J. Vib. Control
, 13
(11
), pp. 1603
–1628
.48.
Cao
, M.
, and Xiao
, J.
, 2008
, “A Comprehensive Dynamic Model of Double-Row Spherical Roller Bearing-Model Development and Case Studies on Surface Defects, Preloads, and Radial Clearance
,” Mech. Syst. Signal Process.
, 22
(2
), pp. 467
–489
.49.
Arslan
, H.
, and Aktu¨rk
, N.
, 2008
, “An Investigation of Rolling Element Vibrations Caused by Local Defects
,” ASME J. Tribol.
, 130
(4
), p. 041101
.50.
Rafsanjani
, A.
, Abbasion
, S.
, Farshidianfar
, A.
, and Moeenfard
, H.
, 2009
, “Nonlinear Dynamic Modeling of Surface Defects in Rolling Element Bearing Systems
,” J. Sound Vib.
, 319
(3–5
), pp. 1150
–1174
.51.
Patil
, M. S.
, Mathew
, J.
, Rajendrakumar
, P. K.
, and Desai
, S.
, 2010
, “A Theoretical Model to Predict the Effect of Localized Defect on Vibrations Associated With Ball Bearing
,” Int. J. Mech. Sci.
, 52
(9
), pp. 1193
–1201
.52.
Nakhaeinejad
, M.
, and Bryant
, M. D.
, 2010
, “Dynamic Modeling of Rolling Element Bearings With Surface Contact Defects Using Bond Graphs
,” ASME J. Tribol.
, 133
(1
), p. 011102
.53.
Patel
, V. N.
, Tandon
, N.
, and Pandey
, R. K.
, 2010
, “A Dynamic Model for Vibration Studies of Deep Groove Ball Bearings Considering Single and Multiple Defects in Races
,” ASME J. Tribol.
, 132
(4
), p. 041101
.54.
Tadina
, M.
, and Boltežar
, M.
, 2011
, “Improved Model of a Ball Bearing for the Simulation of Vibration Signals Due to Faults During Run-Up
,” J. Sound Vib.
, 330
(17
), pp. 4287
–4301
.55.
Kankar
, P. K.
, Sharma
, S. C.
, and Harsha
, S. P.
, 2012
, “Vibration Based Performance Prediction of Ball Bearings Caused by Localized Defects
,” Nonlinear Dyn.
, 69
(3
), pp. 847
–875
.56.
Pandya
, D. H.
, Upadhyay
, S. H.
, and Harsha
, S. P.
, 2013
, “Nonlinear Dynamic Analysis of High Speed Bearings Due to Combined Localized Defects
,” J. Vib. Control
, 20
(15
), pp. 2300
–2313
.57.
Bogdevičius
, M.
, and Skrickij
, V.
, 2013
, “Investigation of Dynamic Processes in Ball Bearings With Defects
,” Solid State Phenom.
, 198
, pp. 651
–656
.58.
Wang
, F.
, Jing
, M.
, Yi
, J.
, and Dong
, G.
, 2014
, “Dynamic Modelling for Vibration Analysis of a Cylindrical Roller Bearing Due to Localized Defects on Raceways
,” J. Multi-Body Dyn.
, 229
(1
), pp. 39
–64
.59.
Liu
, J.
, Shao
, Y.
, and Lim
, T. C.
, 2012
, “Vibration Analysis of Ball Bearings With a Localized Defect Applying Piecewise Response Function
,” Mech. Mach. Theory
, 56
, pp. 156
–169
.60.
Liu
, J.
, and Shao
, Y.
, 2015
, “A New Dynamic Model for Vibration Analysis of a Ball Bearing Due to a Localized Surface Defect Considering Edge Topographies
,” Nonlinear Dyn.
, 79
(2
), pp. 1329
–1351
.61.
Liu
, J.
, Shao
, Y.
, and Zhu
, W. D.
, 2015
, “A New Model for the Relationship Between Vibration Characteristics Caused by the Time-Varying Contact Stiffness of a Deep Groove Ball Bearing and Defect Sizes
,” ASME J. Tribol.
, 137
(3
), p. 31101
.62.
Liu
, J.
, and Shao
, Y.
, 2017
, “Dynamic Modeling for Rigid Rotor Bearing Systems With a Localized Defect Considering Additional Deformations at the Sharp Edges
,” J. Sound Vib.
, 398
, pp. 84
–102
.63.
Moazen Ahmadi
, A.
, Petersen
, D.
, and Howard
, C.
, 2015
, “A Nonlinear Dynamic Vibration Model of Defective Bearings—The Importance of Modelling the Finite Size of Rolling Elements
,” Mech. Syst. Signal Process.
, 52–53
, pp. 309
–326
.64.
Petersen
, D.
, Howard
, C.
, Sawalhi
, N.
, Moazen Ahmadi
, A.
, and Singh
, S.
, 2015
, “Analysis of Bearing Stiffness Variations, Contact Forces and Vibrations in Radially Loaded Double Row Rolling Element Bearings With Raceway Defects
,” Mech. Syst. Signal Process.
, 50–51
, pp. 139
–160
.65.
Niu
, L.
, Cao
, H.
, He
, Z.
, and Li
, Y.
, 2014
, “Dynamic Modeling and Vibration Response Simulation for High Speed Rolling Ball Bearings With Localized Surface Defects in Raceways
,” ASME J. Manuf. Sci. Eng.
, 136
(4
), p. 041015
.66.
Niu
, L.
, Cao
, H.
, He
, Z.
, and Li
, Y.
, 2015
, “A Systematic Study of Ball Passing Frequencies Based on Dynamic Modeling of Rolling Ball Bearings With Localized Surface Defects
,” J. Sound Vib.
, 357
, pp. 207
–232
.67.
Yamamoto
, T.
, and Ishida
, Y.
, 1974
, “The Particular Vibration Phenomena Due to Ball Bearings at the Major Critical Speed
,” Bull. JSME
, 17
(103
), pp. 59
–67
.68.
Yamamoto
, T.
, Ishida
, Y.
, and Kawasumi
, J.
, 1977
, “The Particular Vibration Phenomena Due to Ball Bearings at the Mayor Critical Speed (2nd Report, on the Effects of Symmetrical Nonlinear Spring Characteristics)
,” Bull. JSME
, 20
(139
), pp. 33
–39
.69.
Yamamoto
, T.
, Ishida
, Y.
, Ikeda
, T.
, and Yamada
, M.
, 1981
, “Subharmonic and Summed-and-Differential Harmonic Oscillations in an Unsymmetrical Rotor
,” Bull. JSME
, 24
(187
), pp. 192
–199
.70.
Bai
, C.
, Zhang
, H.
, and Xu
, Q.
, 2013
, “Subharmonic Resonance of a Symmetric Ball Bearing-Rotor System
,” Int. J. Non-Linear Mech
, 50
, pp. 1
–10
.71.
McFadden
, P. D.
, and Smith
, J. D.
, 1984
, “Vibration Monitoring of Rolling Element Bearings by the High-Frequency Resonance Technique—A Review
,” Tribol. Int.
, 17
(1
), pp. 3
–10
.72.
Tandon
, N.
, and Nakra
, B. C.
, 1992
, “Vibration and Acoustic Monitoring Techniques for the Detection of Defects in Rolling Element Bearings—A Review
,” Shock Vib. Dig.
, 24
(3
), pp. 3
–11
.73.
Tandon
, N.
, and Choudhury
, A.
, 1999
, “A Review of Vibration and Acoustic Measurement Methods for the Detection of Defects in Rolling Element Bearings
,” Tribol. Int.
, 32
(8
), pp. 469
–480
.74.
Peng
, Z. K.
, and Chu
, F. L.
, 2004
, “Application of the Wavelet Transform in Machine Condition Monitoring and Fault Diagnostics: A Review With Bibliography
,” Mech. Syst. Signal Process.
, 18
(2
), pp. 199
–221
.75.
Randall
, R. B.
, and Antoni
, J.
, 2011
, “Rolling Element Bearing Diagnostics-a Tutorial
,” Mech. Syst. Signal Process.
, 25
(2
), pp. 485
–520
.76.
Feng
, Z.
, Liang
, M.
, and Chu
, F.
, 2013
, “Recent Advances in Time-Frequency Analysis Methods for Machinery Fault Diagnosis: A Review With Application Examples
,” Mech. Syst. Signal Process.
, 38
(1
), pp. 165
–205
.77.
Sun
, H.
, He
, Z.
, Zi
, Y.
, Yuan
, J.
, Wang
, X.
, Chen
, J.
, and He
, S.
, 2014
, “Multiwavelet Transform and Its Applications in Mechanical Fault Diagnosis—A Review
,” Mech. Syst. Signal Process.
, 43
(1–2
), pp. 1
–24
.78.
Yan
, R.
, Gao
, R. X.
, and Chen
, X.
, 2014
, “Wavelets for Fault Diagnosis of Rotary Machines: A Review With Applications
,” Signal Process.
, 96
(Pt. A
), pp. 1
–15
.79.
El-Thalji
, I.
, and Jantunen
, E.
, 2015
, “A Summary of Fault Modelling and Predictive Health Monitoring of Rolling Element Bearings
,” Mech. Syst. Signal Process.
, 60–61
, pp. 252
–272
.80.
Abboud
, D.
, Antoni
, J.
, Sieg-Zieba
, S.
, and Eltabach
, M.
, 2017
, “Envelope Analysis of Rotating Machine Vibrations in Variable Speed Conditions: A Comprehensive Treatment
,” Mech. Syst. Signal Process.
, 84
, pp. 200
–226
.81.
Feng
, N. S.
, Hahn
, E. J.
, and Randall
, R. B.
, 2002
, “Using Transient Analysis Software to Simulate Vibration Signals Due to Rolling Element Bearing Defects
,” Third Australian Congress on Applied Mechanics
, Sydney, Australia, Feb. 20–22, pp. 689
–694
.82.
Cui
, L.
, Zhang
, Y.
, Zhang
, F.
, Zhang
, J.
, and Lee
, S.
, 2016
, “Vibration Response Mechanism of Faulty Outer Race Rolling Element Bearings for Quantitative Analysis
,” J. Sound Vib.
, 364
, pp. 67
–76
.83.
Randall
, R. B.
, 1987
, Frequency Analysis
, Brüel & Kjær
, Nærum, Denmark
.84.
Chen
, Y. S.
, 2002
, Nonlinear Dynamics
, Higher Education Press
, Beijing, China
.85.
Rigaud
, E.
, and Perret-Liaudet
, J.
, 2003
, “Experiments and Numerical Results on Non-Linear Vibrations of an Impacting Hertzian Contact—Part 1: Harmonic Excitation
,” J. Sound Vib.
, 265
(2
), pp. 289
–307
.86.
Sinou
, J. J.
, 2009
, “Non-Linear Dynamics and Contacts of an Unbalanced Flexible Rotor Supported on Ball Bearings
,” Mech. Mach. Theory
, 44
(9
), pp. 1713
–1732
.Copyright © 2018 by ASME
You do not currently have access to this content.
